Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PETTIS CONDITIONAL EXPECTATION OF CLOSED CONVEX RANDOM SETS IN A BANACH SPACE WITHOUT RNP

  • Akhiat, Fattah (Laboratoire D'Analyse, Geometrie et ApplicationsDepartement de MathematiquesFaculte des Sciences kenitra) ;
  • El Harami, Mohamed (University Moulay Ismail, Higher School of Technology) ;
  • Ezzaki, Fatima (University Sidi Mohamed Ben Abdellah Faculty of Sciences and Technology Laboratory of Modeling and Computing Sciences)
  • Received : 2017.07.22
  • Accepted : 2018.03.08
  • Published : 2018.07.01
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Abstract

In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.

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References

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